Kinetics PDF

KINETICS The Three Laws of Motion are: 1. Newton’s first law of motion - Newton's first law of motion states that, if a body is in the state of rest or is moving with a constant speed in a straight line, then the body will remain in the state of rest or keep moving in the straight line,...

KINETICS The Three Laws of Motion are: 1. Newton’s first law of motion - Newton's first law of motion states that, if a body is in the state of rest or is moving with a constant speed in a straight line, then the body will remain in the state of rest or keep moving in the straight line, unless and until it is acted upon by an external force. 2. Examples :- 1. Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator. 2. The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface. 3. To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted. 4. Headrests are placed in cars to prevent whiplash injuries during rear-end collisions. 5. While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting rock or other object that abruptly halts the motion of the skateboard. 6. Newton’s second law of motion - Newton's 2nd law of motion states that “ the rate of change of momentum of a body is directly proportional to the force applied on it, and the momentum occurs in the direction of the net applied force F= p = momentum Or F = ma m= mass , a = acceleration Where ‘F’ is the applied force, ‘a’ is the acceleration produced, and m is the mass of the object.” 7. Newton’s third law of motion – According to Newton's third law of motion, to every action, there is always an equal and opposite reaction. Let two bodies 1 & 2 are in interaction with each other, then F12 = -F21 (force on body 2 by 1) = - (force on body 1 by 2) Momentum - It is defined as the quantity of motion contained in a body. It is measured as the product of mass of the body and its velocity and has the same direction as that of the velocity. It is a vector quantity. It is represented by p. The SI unit of momentum is kg-m/s.  p = mv Suppose you catch a cricket ball and a tennis ball when dropped from the same height. We find that it is easier to catch a tennis ball than a cricket ball. This determines that mass is an important factor that determines the effect of force on its motion. Force When we look around us and observe the state of rest or motion of bodies, we find that nothing moves on its own. When we push or pull a body, It may change its state of rest or of uniform motion. It may change its direction of motion. It may change its shape. We say that we exert a force on a body if we push or pull it. This push or pull may be gentle or hard, so force has a magnitude. This push or pull may be in different directions, so force has a direction. It means force is a vector quantity. The SI unit of force is newton represented by 'N'. The CGS unit of force is dyne. Note : 1N = 105 dyne thus we can define, Force - is an entity which when applied on a body changes or tends to change a body’s, State of rest, State of uniform motion, Direction of motion and Shape. SI unit – newton (N) CGS Unit- dyne Application of Newton's Second Law of Motion - 1. Cricket player lowers his hand while catching the ball : The player increases the time during which the high velocity of moving ball reduces to zero. If we increase time , Force decreases, so force on palm of the fielder reduces. 2. A karate player can break a pile of tiles with a single blow of his hand : Because he strikes the pile of tiles with his hand very fast, during which the entire momentum of the fast moving hand is reduced to zero in very short interval of time. This exerts a very large force on the pile of tiles which is sufficient to break them, by a single blow of his hand. 3. In a high jump athletic event, the athletes are allowed to fall either on a sand bed or cushioned bed : This is because to increase the time of athletes fall to stop after making the high jump, which decreases rate of change of momentum and decreases force of impact. Impulse The product of force and time, which is also the change in momentum of the body is called impulse. Impulse = Force × time duration = Ft = Change in momentum Action and Reaction When there is a force exerted by body 1 on body 2, there is also a force exerted by body 2 on body 1. These forces are equal in magnitude and act in opposite directions. Such a pair of forces is called an action-reaction pair. Any of the two forces may be called the action, the other will be the reaction. Applications of Third Law Recoiling of a gun : When a bullet is fired from a gun, it exerts a forward force on the bullet and the bullet exerts an equal and opposite force on the gun. Due to the high mass of the gun, it moves a little distance backward and gives a backward jerk to the shoulder of the gunman. To walk, we press the ground in backward direction with foot : When we walk on the ground, our foot pushes the ground backward and in return the ground pushes our foot forward. Significance of Newton’s Laws 1. The first law talks about the natural state of motion of a body, i.e., motion along a straight line with constant speed. 2. The second law says that if a body is not following its natural state of motion, then there has to be net unbalanced external force acting on the body. 3. The third law talks about the nature of the force, i.e., forces exist in pairs. Conservation of Momentum According to conservation law of linear momentum, “The total momentum of an isolated system of interacting particles is conserved.” In other words, “for an isolated system the initial momentum of the system is equal to the final momentum of the system”. Consider two objects A and B of masses m1 and m2 moving along the same direction at different velocities u1 and u2 respectively. m1u1 + m2u1 = m1v1 + m2v2 Total momentum before collision = Total momentum after collision Applications of Law of Conservation of Linear Momentum (i) Recoil Velocity of a Gun (ii) Rocket propulsion Various Forces in Nature In mechanics, we come across a variety of forces, like the weight of a body or the force exerted by a stretched spring. (i) Weight Weight is the gravitational force with which the earth pulls an object. The weight of an object is F = mg Where, g - is acceleration due to gravity. The weight of a body is a force acting on the body towards the centre of earth. Work – the work is said to be done if a force exerted on an object, causes the displacement of the object in the direction of the force. The work done is given by, F = force exerted and s = displacement caused SI unit – joule Work has only magnitude and no direction. Hence, work is a scalar quantity. Formula of Work The work done by a force is defined to be the product of the component of the force in the direction of the displacement and the magnitude of this displacement. Where W is the work done, F is the force, s is the displacement, θ is the angle between force and displacement and F cosθ is the component of force in the direction of displacement. We understand from the work equation that if there is no displacement, there is no work done, irrespective of how large the force is. To summarize, we can say that no work is done if: the displacement is zero the force is zero the force and displacement are mutually perpendicular to each other. Power – The rate at which work is done is called as power. W = work done , t = time SI Unit - watt Energy - energy is defined as the capacity to do work. Energy can be of two types - 1) kinetic energy 2) potential energy 1) Kinetic energy - the energy possessed by a moving object is called kinetic energy. m = mass of object, v = velocity of the object. 2) Potential energy – the energy possessed by the object due to its position is called as Potential energy. P.E. = mgh m = mass of object, g= acceleration due to gravity = 9.8 m/s2